Let us refer the interested reader to the book [1]} for
technical details and only give the following list of basic expansions:
\(&&{g^{\prime }}^{\mu \nu } = g^{\mu \nu }-h^{\mu \nu }+h^\mu _{\,\,\lambda } h^{\nu \lambda }-h^\mu _{\,\,\lambda } h^\lambda _{\,\,\tau } h^{\nu \tau } + ..\nonumber \\&&\sqrt{- g^\prime } = \sqrt{- g} \, \Big ( 1 + \frac{1}{2}\,h+\frac{1}{8}\,h^2 - \frac{1}{4}\,h_{\mu \nu }h^{\mu \nu } + \,...\Big ),\nonumber \\&&{\Gamma ^\prime }^\alpha _{\,\,\beta \gamma } \,=\,\Gamma ^\alpha _{\,\,\beta \gamma } + \delta \Gamma ^\alpha _{\,\,\beta \gamma }\,,\) 
